Reflecting on last season's agonising semi-final exit to Paris Saint-Germain in an interview with MARCA at the Allianz Arena, Kane looked back on a campaign he described as historic.
"Last season was really good for us: second in the league phase, with seven wins and one defeat. And then we had some very good matches: Atalanta, Real Madrid... that one was really special, and against PSG, of course.
"Two incredible matches for the fans. Our narrow defeat was hard to take. We were so close, we had the confidence and quality to be in the final.
"But that's the Champions League: everything is decided by the smallest margins," Kane said.
Asked about this season's ambitions, with the final due to be played in Madrid, Kane said Bayern Munich's hunger remained intact.
"It's about doing more or less the same thing, and conquering that final step. This Bayern side has the hunger it needs as a group, as a team, and also the right coach."
Bayern will face Atlético Madrid in the league phase, a side Kane has never previously faced.
"Atlético have shown how good they can be. They reached the semi-finals last Champions League, and they have all my respect: it will be a difficult match but we'll be prepared. At that stadium (the Metropolitano) I lost a Champions League final with Tottenham, and it was a tough moment. I hope to go back there and have a different story."
On his remarkable scoring record at 32, Kane credited his personal sports doctor.
"One of them you know well [Kane refers to Alejandro Elorriaga, his Madrid-born personal sports doctor]. Alejandro has played a very important role in my success... We've been together six and a half years now [since March 2020] and he's one of the main reasons I can perform at this level and play so many matches."
On the Ballon d'Or, for which he is a leading contender after scoring 73 goals in 65 appearances for club and country last season, Kane was characteristically reluctant to campaign for himself.
"It's complicated. I've never liked talking too much about myself. The only thing I'd say is that last season was incredible, personally and as a team. It was by far the best season of my life... But the Ballon d'Or isn't in my hands. It depends on the people who vote."
Kane also spoke warmly of his old Tottenham manager, José Mourinho, now in charge of Real Madrid.
"I adore José. We had a really good relationship at Tottenham. It didn't end the way we wanted... I got a lot of freedom to be myself, to play and to drop deep and receive the ball. He understands every detail of the game."
Reflecting on England's World Cup semi-final defeat by Argentina, Kane recalled embracing Lionel Messi afterwards.
"I have enormous respect for Messi. I saw him grow as a footballer... That day, after losing, I tried to keep my head high and show respect for the other team."
Kane closed by crediting his family for underpinning his longevity in the game.
"I think stability in your family life isn't talked about enough in professional football, especially for young players... I've been very lucky to have found my wife, who I even went to school with, and to have my parents, my brother and my in-laws here. They're my biggest support."